const GF2 ConstTerm(const GF2X& a)
{
if (IsZero(a))
return to_GF2(0);
else
return to_GF2((a.xrep[0] & 1) != 0);
}
const GF2 LeadCoeff(const GF2X& a)
{
if (IsZero(a))
return to_GF2(0);
else
return to_GF2(1);
}
const GF2 coeff(const GF2X& a, long i)
{
if (i < 0) return to_GF2(0);
long wi = i/NTL_BITS_PER_LONG;
if (wi >= a.xrep.length()) return to_GF2(0);
long bi = i - wi*NTL_BITS_PER_LONG;
return to_GF2((a.xrep[wi] & (1UL << bi)) != 0);
}
const GF2 vec_GF2::get(long i) const
{
const vec_GF2& v = *this;
if (i < 0 || i >= v.length())
LogicError("vec_GF2: subscript out of range");
long q = i/NTL_BITS_PER_LONG;
long p = i - q*NTL_BITS_PER_LONG;
if (v.rep[q] & (1UL << p))
return to_GF2(1);
else
return to_GF2(0);
}
const GF2 GF2X::operator[](long i) const
{
if (i < 0) LogicError("GF2X: subscript out of range");
long wi = i/NTL_BITS_PER_LONG;
if (wi >= xrep.length()) LogicError("GF2X: subscript out of range");
long bi = i - wi*NTL_BITS_PER_LONG;
return to_GF2((xrep[wi] & (1UL << bi)) != 0);
}
void ident(mat_GF2& X, long n)
{
X.SetDims(n, n);
clear(X);
long i;
for (i = 0; i < n; i++)
X.put(i, i, to_GF2(1));
}
NTL_START_IMPL
GF2 power(GF2 a, long e)
{
if (e == 0) {
return to_GF2(1);
}
if (e < 0 && IsZero(a))
ArithmeticError("GF2: division by zero");
return a;
}
void inv(GF2& d, mat_GF2& X, const mat_GF2& A)
{
long n = A.NumRows();
if (A.NumCols() != n)
Error("solve: nonsquare matrix");
if (n == 0) {
X.SetDims(0, 0);
set(d);
}
long i, j, k, pos;
mat_GF2 M;
M.SetDims(n, 2*n);
vec_GF2 aa;
aa.SetLength(2*n);
for (i = 0; i < n; i++) {
aa = A[i];
aa.SetLength(2*n);
aa.put(n+i, 1);
M[i] = aa;
}
long wn = ((2*n) + NTL_BITS_PER_LONG - 1)/NTL_BITS_PER_LONG;
for (k = 0; k < n; k++) {
long wk = k/NTL_BITS_PER_LONG;
long bk = k - wk*NTL_BITS_PER_LONG;
_ntl_ulong k_mask = 1UL << bk;
pos = -1;
for (i = k; i < n; i++) {
if (M[i].rep.elts()[wk] & k_mask) {
pos = i;
break;
}
}
if (pos != -1) {
if (k != pos) {
swap(M[pos], M[k]);
}
_ntl_ulong *y = M[k].rep.elts();
for (i = k+1; i < n; i++) {
// M[i] = M[i] + M[k]*M[i,k]
if (M[i].rep.elts()[wk] & k_mask) {
_ntl_ulong *x = M[i].rep.elts();
for (j = wk; j < wn; j++)
x[j] ^= y[j];
}
}
}
else {
clear(d);
return;
}
}
vec_GF2 XX;
XX.SetLength(2*n);
X.SetDims(n, n);
clear(X);
for (j = 0; j < n; j++) {
XX.SetLength(n+j+1);
clear(XX);
XX.put(n+j, to_GF2(1));
for (i = n-1; i >= 0; i--) {
XX.put(i, XX*M[i]);
}
XX.SetLength(n);
AddToCol(X, j, XX);
}
set(d);
return;
}
